Conical spring

ABSTRACT

A conical spring is provided wherein the diameters of the coils thereof vary progressively, and the spaces separating adjacent coils vary in relation to the dimensions of the coils to provide predetermined force-displacement spring characteristics.

United States Patent 11 1 Beery et al.

[ Aug. 7, 1973 l (TONICAL SPRING I75] Inventors: Jack Beery, Farmington;Zong S.

Luo, Plymouth, both of Mich.

[731 Assignec: Burroughs Corporation, Detroit,

Mich.

221 Filed: Nov. 1, 1971 211 Appl.No.: 194,104

[52] US. Cl. 267/166, 267/180 [5 l] Int. Cl Fl6f 1/06 [58] Field ofSearch 267/180, 177, 168,

[56} References Cited UNITED STATES PATENTS 2,650,617 9/]953: Wasscr267/l80 Powers t i 1 1 i i 1 5/256 Spangenbcrg 267/l77 PrimaryExaminer-lames B. Marbert Attorney Paul W. Fish and Edwin W. Uren 5 71ABSTRACT A conical spring is provided wherein the diameters of the coilsthereof vary progressively, and the spaces separating adjacent coilsvary in relation to the dimensions of the coils to provide predeterminedforcedisplacement spring characteristics.

2 Claims, 3 Drawing Figures l CONICAL SPRING BACKGROUND OF THE INVENTIONThe invention relates to helical springs in general and moreparticularly to conically shaped springs.

Prior art discloses springs having restoring forces which varyunpredictably with respect to changes in spring displacement withintheir respective operating ranges. The designs of many of these springshave substantially empirical histories, having often been designed onlyto exert some minimum restoring force in response to some arbitrarydisplacement or to provide restoring forces within some maximum range ofvalues in response to displacement within certain limits.

SUMMARY OF THE INVENTION The invention resides in the provision of aconical spring design which embraces specific relationships between thephysical dimensions, disposition and characteristics of a springmaterial to predetermine the restoring force which will be exerted bythe spring in response to any given displacement thereof.

Accordingly, it is an object of the present invention to provide aconical spring having a restoring force which is a mathematicallydeterminable function of any given displacement of the spring.

An important aspect of the invention is the use of a conical springdesign which relates specific physical factors of spring construction toprovide a spring having predetermined force-displacementcharacteristics.

BRIEF DESCRIPTION OF THE DRAWINGS DETAILED DESCRIPTION OF THE INVENTIONThe conical spring shown by FIGS. 1 and 2 has a series of resilientcoils which are mutually adjacent and coaxially disposed. Asillustrated, the coils have progressively varying diameters so that theycollectively form a conical spring. As also shown, the spaces separatingadjacent coils of the spring are varied in relation to the dimensions ofthe coils.

A more rigorous description of the spring and its characteristics isprovided by reference to mathematical notation. From the book titledStrength of Materi als, by S. Timoshenko, the axial, longitudinal,deflection of a helical spring may be expressed by the equation whereinn represents the number of coils, P represents the shearing force, Rrepresents the mean radius of a cylindrical surface containing thecenter line of the spring, G represents the modulus of elasticity inshear of the spring material, 1, represents the polar moment of inertiaof a circular cross section of the spring and is equal to 1rdl32, drepresenting the diameter of the spring material, and or represents theangle of twist of an element between two adjacent cross sections of thespring. If L/a, where L represents the active free length of the springand B represents the average distance between adjacent coils, issubstituted for n in the Timoshenko equation [I] and 'zrdl32 issubstituted for 1,, the equation becomes spring haspreviously beenderived it may be substituted for 8, yielding the equation K d ce/64m.

The radius R, previously defined as being the mean radius of acylindrical surface containing the center line of the spring,may also bedefined by the equation wherein D, represents the outside diameter ofthe spring at a point along its axis. The cube of this would be Rferrer/c 11 and, since the spring index C is defined as c X/d,

then

R d /8(l) Substituting this equation [9] fgr R in the equation [5] forthe minimum: of elasticitfwould yield the equation K dGB/8L(C-I Theoutside diameter of the spring at a point along its longitudinal axismay be defined by the equation OX Di (Df-Di/L 1,

wherein I), represents the smallest outside diameter of the spring, 1),represents the largest outside diameter of the spring and x representssome point along the longitudinal axis of the spring, its value beingbetween or including and that of L. The parenthesized portion of thisequation represents the rate of change of the diameter of the springwith respect to its axial length.

Solving the equation of the bulk modulus of elasticity for B would yieldthe equation wherein the notation B, has been used in place ofB torepresent variable coil pitch, which is the distance between adjacentcoils at some point x along the longitudinal axis of the spring. Thenotation C, has been used in place of C to represent a variable springindex, and it identifies C as being a function of some point x along thelongitudinal axis of the spring at which the equation is to be applied.Since the variable C, has been substituted for D /d, it may be morerigorously defined by substituting therein the mathematical definitionof D to obtain the equation (3,, Di/d (Df-Di)/dL x.

It may be observed at this point that the last two equations [12 and 13]represent a means for determining the physical parameters of a conicalspring having a length equal to the sum of the variable coil pitches B,.If a spring having a different, specific length is required, thefollowing equation may also be solved to determine the actual distancebetween adjacent coils at a particular point 2: along the longitudinalaxis of the spring, that is, to determine the true pitch 5,:

wherein the parenthesized portion of this equation represents thedifference between the desired, active free length of the spring and thelength resulting from summing the variable coil pitches. The ratiofollowing the parenthesized portion indicates what percentage of theaforementioned difference need be added to the variable coil pitch fl,to obtain the true pitch 8,, the sum of which will be the desired freelength.

The last three equations l2, l3 and 14], then, represent a means fordetermining the parameters of a conical spring having physicalcharacteristics as desired. A typical design application would be onewhere the restoring force of a spring is to be a linear function of itsdisplacement, as shown by FIG. 3, although these equations areapplicable to many other design requirements. As in any mathematicallydefined method for design, appropriate known values may be applied tothe equations and desired but unknown design information derived upontheir solution.

While the conical spring has been shown and described in considerabledetail, it should be understood that many changes and variations maybemade therein without departing from the spirit and scope of theinvention.

What is claimed is:

l. A conical spring having a series of mutually adjacent, coaxiallydisposed, resilient coils of progressively varying diameters, saidspring providing predetermined restoring force characteristics relativeto applied displacement forces as determined by the physical dimensionsand disposition of said coils and by the characteristics of thematerials forming said coils, said predetermined restoring forcecharacteristics relative to said applied displacement forces beingderived from the formation and disposition of said coils according tothe equation B 8LK/dG (C, 1) AND C,,= Di/d (DF iNdL x, B representingthe variable coil pitch, K representing the bulk modulus of elasticityof the spring material, G representing the rnodulus of elasticity inshear of the spring material, L representing the active free end of thespring material, C 1 representing a variable spring index, drepresenting the diameter of the spring material, D representing thesmallest outside diamt rof thymine Q; ts r ssntinsllely estp i diameterof the spring, and x representing a variable of length designatinglongitudinal position along the axis of the spring.

2. The conical spring as defined by claim 1 wherein said predeterminedrestoring force characteristics relative to applied displacement forcesas determined by the physical dimensions and disposition of said coilsare derived by the formation of said coils according to the equation beequal to the active free length of the spring.

UNITED STATES PATENT OFFICE I CERTIFICATE OF CORRECTION Patent No. 3 751025 D d August 7 1973 Inventor) Jack Beery et a1.

It is certified that error appears in the above-identified patent andthat said Letters Patent are hereby corrected as shown below:

Column 2, line 8, "L/a" should read L/)3 line 26,

"K P/ f/ sshould read K= P/g line 52, "C =X/d" should read C =D /dSigned and sealed this 8th day of January 1974.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. RENE D. TEGTMEYER Attesting Officer ActingCommissioner of Patents PM PD-1050 (10-69) USCOMM-DC 60376-P69 u.s.sovznunnq' PRINTING OFFICE up o-us-au.

1. A conical spring having a series of mutually adjacent, coaxiallydisposed, resilient coils of progressively varying diameters, saidspring providing predetermined restoring force characteristics relativeto applied displacement forces as determined by the physical dimensionsand disposition of said coils and by the characteristics of thematerials forming said coils, said predetermined restoring forcecharacteristics relative to said applied displacement forces beingderived from the formation and disposition of said coils according tothe equation Bx 8LK/dG (Cx- 1)3AND Cx Di/d + (Df- Di)/dL x, BXrepresenting the variable coil pitch, K representing the bulk modulus ofelasticity of the spring material, G representing the modulus ofelasticity in shear of the spring material, L representing the activefree end of the spring material, CX representing a variable springindex, d representing the diameter of the spring material, Direpresenting the smallest outside diameter of the spring, Dfrepresenting the largest outside diameter of the spring, and xrepresenting a variable of length designating longitudinal positionalong the axis of the spring.
 2. The conical spring as defined by claim1 wherein said predetermined restoring force characteristics relative toapplied displacement forces as determined by the physical dimensions anddisposition of said coils are derived by the formation of said coilsaccording to the equation